Just in case. I do not know the rule about "PGWP under public policy" (one-time countermeasure against the pandemic which could be obtained even after getting into another school after expiration of the 1st PGWP, if conditions were satisfied), but generally, PGWP does not allow to study. It says "Unless authorized, prohibited from attending any educational institution, or taking any academic, professional or vocational training course."
Therefore, Study Permit is useless after PGWP, even before expiration date printed on it.
This is still not true. I am not trying to be antagonistic or anything like that, just trying to clarify and get the information out there because I had the same wrong information about concurrent PGWP and Study Permit before I got mine.
What I am discussing here is not a one-time public policy. Apparently, this is how it has always been: that you can hold both a PGWP for a just ended study (say you just finished an Msc) and a study permit for a new study (say you just got admiitrd into a PhD following my Msc) and both are valid concurrently. The only limitation is that you only get PGWP once in a lifetime, so the border officer will ask you twice if you are sure that you don't want to wait for you to finish your PhD before getting the PGWP.
As a matter of fact, the border officer explained the quote above that 'Unless authorized, prohibited from attending any educational institution, or taking any academic, professional or vocational training course.", Unless authorized means that unless you have a Study Permit you can't study while you are on PGWP. So he said that for you to study at the same time while you have a valid PGWP you must apply for a study permit.
Just in case you are wondering if this is a mistake or something, I renewed both my PGWP and Study Permit just last week online. They were previously issued to my passport expiry but I got a new passport and now they expire in 2024.
TL;DR: YOU can have both PGWP and Study Permit at the same time and it's not a one-time public policy. Read the clause you wrote above again slowly from the beginning and you will see why this is correct. "Unless authorized,"